Pinching-Antenna Systems (PASS) Aided Over-the-air Computation

Haoyun Li; H. Vincent Poor; Ming Xiao; Yulan Gao; Zhonghao Lyu

REVIEW 1 major objections 5 minor 3 cited by

Pinching-Antenna Systems (PASS) Aided Over-the-air Computation

T0 review · 1 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Jointly optimizing pinching-antenna positions, transmit power, and decoding vector minimizes AirComp MSE and beats fixed, discrete, and conventional MIMO benchmarks.

desk verdict Plausible but incremental PASS-AirComp paper whose power-update formula omits nonnegativity and may inflate the reported MSE gains; fixable, worth a referee. read the letter →

arxiv 2505.07559 v1 pith:7L7RCXH2 submitted 2025-05-12 cs.IT eess.SPmath.IT

Zhonghao Lyu , Haoyun Li , Yulan Gao , Ming Xiao , H. Vincent Poor This is my paper · ORCID

classification cs.ITeess.SPmath.IT

keywords pinchingantennasystemsover-the-aircomputationmeansquarederrorjointoptimizationalternatingGauss-Seidelwirelessdataaggregation6Gedgeintelligence

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper proposes a pinching-antenna system (PASS) for over-the-air computation (AirComp), in which a base station's antennas are passive elements that slide along dielectric waveguides to reshape the wireless channel. It tries to show that jointly choosing the antenna positions, the users' transmit powers, and the decoding vector substantially reduces the mean-squared error (MSE) of the aggregated sum. The authors formulate this as a highly non-convex optimization problem and solve it with an alternating-optimization framework whose position updates run a Gauss-Seidel scan with a one-dimensional grid search per antenna. Simulation results across waveguide length, number of antennas, and number of users show the joint design outperforms fixed positions, conventional MIMO with the same number of RF chains, discrete activation, and projected-gradient position optimization. If correct, this makes AirComp accuracy a tunable, largely passive hardware property rather than something fixed by the propagation environment.

What carries the argument

The load-bearing object is the equivalent channel coefficient $g_{m,k}(\tilde{\mathbf{v}}_m)$ in Eq. (6): the sum over the $N$ pinching antennas on waveguide $m$ of an isotropic free-space path loss and phase, multiplied by the waveguide propagation phase $e^{-j 2\pi i_{\mathrm{ref}} v_{m,n}/\lambda}$ accumulated to the feed point. This single scalar per user-waveguide pair turns antenna placement into a continuous design variable, and it is what makes position-based beamforming possible. The optimization machinery is alternating optimization: $w$ from a closed-form least-squares solution, $\mathbf{P}$ from a convex quadratically constrained quadratic program solved by KKT conditions, and each $v_{m,n}$ from a scalar objective minimized by grid search over the feasible interval, with the minimum-spacing constraint enforced by trimming the search region.

What would settle it

Build a 28 GHz PASS prototype with four waveguides, two pinching antennas per waveguide, and three users; measure the MSE for optimized versus fixed antenna positions under the paper's channel model. If the model's predicted phase and amplitude at the feed point do not match measurements, or if the optimized positions do not lower the measured MSE, the central claim is refuted.

Watch

Extended reading notes

Core claim

The central claim is that PASS-aided AirComp with jointly optimized pinching-antenna positions, transmit powers, and decoding vector achieves lower aggregation MSE than the natural benchmarks. The channel from a user to a waveguide's feed point is modeled as a coherent sum of line-of-sight contributions from each pinching antenna, each carrying a free-space phase plus a waveguide propagation phase. Because antenna position enters both amplitude and phase, the MSE objective is highly non-convex; the paper's contribution is to show that an alternating scheme—closed-form decoding vector, closed-form power update, and Gauss-Seidel position refinement over a discrete grid—converges and beats fixed-antenna, conventional-MIMO, discrete-PASS, and projected-gradient designs in simulation. The improvement grows with waveguide length and with the number of pinching elements per waveguide, and widens as the number of users increases.

Load-bearing premise

The channel model assumes each pinching antenna receives a clean line-of-sight signal and that the waveguide adds all antenna signals at the feed point with only a propagation phase—no attenuation, no mutual coupling, no hardware loss—and that user locations and channel states are known perfectly.

Editorial extensions

If this is right

Longer waveguides lower the aggregation MSE because the antennas have more room to move close to users; the same hardware can serve a wider area with the same number of RF chains.
Adding more pinching antennas per waveguide keeps improving MSE, whereas fixed-placement antennas saturate, so the benefit comes from optimization, not just element count.
The performance gap over benchmark schemes grows with the number of users, suggesting PASS is most valuable precisely when AirComp alignment is hardest.
Since pinching antennas are passive and repositioning requires no electrical reconnection, the proposed design improves accuracy without additional transmit power or RF hardware.
The algorithm converges in about 15 iterations, so the joint design is practical enough for dynamic environments that need frequent re-optimization.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the ideal coherent-summation channel model holds in hardware, the same position-optimization principle should extend to other AirComp target functions and to imperfect channel-state information, where robust position design could trade a little MSE for resilience.
A direct testable extension is to compare PASS against movable-antenna arrays under the same user distributions, isolating whether continuous movement along waveguides or two-dimensional antenna displacement matters more for AirComp.
The grid-search position update is a quantization step; replacing it with a continuous local solver could squeeze further gains, at the cost of more computation per iteration.
If realized at scale, PASS-aided AirComp could lower the hardware cost of federated edge learning by replacing active phase control with passive placement.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Two things to know. First, this is a credible incremental application of pinching antennas to over-the-air computation, with a competent alternating-optimization setup. Second, the transmit-power update in Eq. (20) is missing the nonnegativity constraint on p_k and can return negative square-root powers, which would artificially lower the MSE. That is a real bug, not a modeling choice.

What is actually new: the paper is the first to combine PASS with AirComp, optimizing PA positions, user powers, and the combiner. The channel model follows the PASS literature. The benchmarks are reasonable in the equal-RF-chain sense, and the Gauss-Seidel position search with the scalarized subproblem is a sensible way to handle the non-convex position optimization. The MSE expression and the convergence argument are coherent.

The soft spots, in proportion. The power-update issue is the load-bearing one. Problem (P1) implicitly requires p_k >= 0 because p_k is a transmit power, but the Lagrangian and KKT only enforce P^2 <= P_max. The closed form P_kk = Re(w^H g_k)/(|w^H g_k|^2 + lambda_k) becomes negative whenever the real part is negative; nothing clips it. Since the MSE separates over users, a negative sqrt-power genuinely reduces the objective relative to the feasible optimum. The authors need to add the lower-bound multiplier or clamp to zero and re-run the simulations; until then, the reported gains over the benchmarks are not fully supported.

Secondary issues are minor: the grid resolution L for the PA position search is not reported, the convergence threshold is not given, and there is no code or error bars. The 300-realization averaging is adequate but more transparency would help.

The channel model assumes lossless coherent summation in the waveguide, which is taken directly from the PASS papers. It is an idealization, but I would not single it out as a flaw here.

Who is this for: people working on AirComp for edge AI and anyone tracking PASS applications. It is an incremental but legitimate extension, not a field-opener.

Recommendation: I would send it out. A good referee can ask for the nonnegativity fix and a clean re-run, and if the gains survive, the paper is a fine letter. If the gains vanish, then the reader learns something about PASS-AirComp.

Bring it to reading group only if you care about this specific area; otherwise skim the figures.

Referee Report

1 major / 5 minor

Summary. This paper proposes a pinching-antenna-system (PASS) aided over-the-air computation (AirComp) design. The base station is equipped with M dielectric waveguides, each with N pinching antennas, and serves K single-antenna users. The authors formulate an MSE minimization problem that jointly optimizes the PA positions, the user transmit powers, and the decoding vector, subject to per-user power limits and minimum PA spacing. They develop an alternating optimization framework: a closed-form MMSE update for the decoding vector, a KKT-based closed form for the transmit powers, and a Gauss-Seidel coordinate-descent with grid search for the PA positions. Numerical results in Section IV show that the proposed design outperforms fixed-PA, conventional MIMO, discrete-PASS, and PGD-based benchmarks.

Significance. The paper brings the emerging PASS technology to AirComp, offering a passive, reconfigurable, and low-cost way to reshape channels for computation. If the optimization framework were correct, the paper would be a timely contribution to both the PASS and AirComp literatures, and the benchmark comparisons are reasonably fair in terms of RF-chain count. However, the transmit-power update contains a load-bearing flaw that may invalidate the numerical evidence. Because the reported superiority over benchmarks is the central claim, the significance of the paper is contingent on fixing this issue.

major comments (1)

[III-2, Eqs. (16)–(21)] The Lagrangian (16) and KKT conditions (17)–(19) for the power subproblem (P3) only enforce the upper-bound constraint P^2 ≼ P_max and omit the physical nonnegativity constraint p_k ≥ 0, equivalent to P_kk ≥ 0. The closed-form solution (20) gives P_kk = Re((G^H w)_k)/(|w^H g_k|^2 + λ_k), which is negative whenever Re((G^H w)_k) < 0. Since P = diag(√p_k) with √p_k ≥ 0 is the transmitted amplitude, negative P_kk is not physically realizable and effectively introduces a spurious phase shift of π for those users, which can lower the MSE objective compared to the true constrained optimum. The projection in (21) only forces Λ ⪰ 0 and does not restore P to the nonnegative orthant. Consequently, Algorithm 1 may return infeasible power vectors, and the MSE gains reported in Section IV could be inflated. The authors must either add the explicit constraint P ⪰ 0 and re-derive the KKT solution, or allow complex transmit coefficients with magnitude √p_k and reformulate the problem accordingly. They should also report whether negative P_kk arises in their simulations and, if so, quantify its effect on the results.

minor comments (5)

[IV, Eq. (29)] The grid resolution L used for the PA position grid search is never specified in the numerical results. Since the PA positions are optimized over a discrete set, L affects the attained solution and the fairness of comparison with the discrete-PASS benchmark (which uses 300 positions). Please report the value of L for each figure.
[II, Eqs. (2)–(6)] The channel model assumes lossless waveguides with only a phase shift in the coherent summation and neglects mutual coupling beyond the minimum spacing L0. These idealizations should be stated explicitly in the system model, and the authors should discuss their potential impact on the practical gains relative to the MIMO benchmark.
[IV, Fig. 2(c)] The horizontal axis of Fig. 2(c) is labeled 'Number of PAs'; please clarify whether this is N per waveguide or the total number of PAs M×N, and describe how the MIMO benchmark is adjusted when N changes.
[III-3, Algorithm 1] The convergence claim relies on monotonic non-increase of the objective, but the PA position update in Step 7 is performed via grid search. If the grid is coarse, the resulting update may not decrease the objective. Please state the terminating threshold ε and specify the grid resolution used.
[Throughout] There are several typographical and formatting artifacts (e.g., 'P ASS', 'rec on-ﬁgurable') that should be cleaned in the final version.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the MSE optimization is self-contained and benchmark comparisons are independently defined.

full rationale

The paper's central claim is a numerical optimization result: it minimizes the MSE in Eq. (10) over V, P, and w subject to constraints (11), with benchmark schemes that fix or differently constrain the same variables. The objective, channel model, and constraints are specified independently of the results, and the alternating updates are derived from that objective: w via the convex least-squares solution (14), P via KKT conditions (17)-(21), and V via the scalar subproblem (P6) solved over an explicit grid (29)-(31). No parameter is fitted to the reported MSE curves and then renamed a prediction. The only references to prior work are contextual: the PASS concept ([9],[10]) and the simulation parameter setup 'similar to that in [11], [12]' (Section IV). These citations are not used as load-bearing evidence for the claimed MSE gains, and no uniqueness theorem or ansatz is imported from the authors' previous papers to forbid alternative designs. The superiority claim is a plausible consequence of optimizing additional spatial degrees of freedom, not a circular reduction. (A separate, non-circular correctness concern is that the KKT power update in (20)-(21) omits the p_k >= 0 lower bound and could return infeasible negative transmit powers; this would affect the validity of the simulations, but it does not make the derivation circular.)

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The central claim rests on a highly idealized physical channel model (LoS, lossless waveguide combining) and on perfect knowledge assumptions. No new physical entities are introduced; PASS itself is prior art. The only hand-chosen numerical parameter that is not disclosed is the grid resolution L, which affects the reported performance.

free parameters (1)

Grid resolution L for PA position search = Not specified in the paper
The PA-position subproblem (P6) is solved by discretizing [0, L_x] into L equally spaced points, but no value of L is reported. The quality and monotonicity of the AO iterations depend on this hand-chosen number, and it is not stated in the simulation setup.

assumptions (4)

domain assumption Free-space LoS channel model with a single path, no small-scale fading or scattering, as in Eq. (2)
Every channel coefficient between a user and a PA is modeled as a deterministic LoS spherical wave. This ignores multipath, blockage, and shadowing, which are common in many wireless environments.
domain assumption Ideal passive waveguide combining: PA signals add coherently at the feed point with only a guided propagation phase and no insertion loss, Eq. (4)-(6)
The model sums all PA signals on a waveguide without attenuation or coupling losses. Real PASS hardware may have non-negligible loss and non-ideal combining.
domain assumption Perfect CSI and exact knowledge of PA positions and user coordinates
The optimizer uses the true channel G(V) and positions; no estimation error or feedback delay is modeled. This is not stated explicitly but is assumed throughout Section III.
domain assumption Data symbols are independent zero-mean unit-variance CSCG and noise is AWGN with variance sigma^2
These are standard information-theoretic assumptions used to derive the MSE expression in Eq. (10); they justify the expectation and the MMSE form of w*.

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Cite this review

Pith. "Pith review of Pinching-Antenna Systems (PASS) Aided Over-the-air Computation." pith.science (2026). https://pith.science/paper/7L7RCXH2

@misc{pith2026250507559,
  author       = {Pith},
  title        = {Pith review of: Pinching-Antenna Systems (PASS) Aided Over-the-air Computation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7L7RCXH2}},
  note         = {Machine review of arXiv:2505.07559}
}

read the original abstract

Over-the-air computation (AirComp) enables fast data aggregation for edge intelligence applications. However the performance of AirComp can be severely degraded by channel misalignments. Pinching antenna systems (PASS) have recently emerged as a promising solution for physically reshaping favorable wireless channels to reduce misalignments and thus AirComp errors, via low-cost, fully passive, and highly reconfigurable antenna deployment. Motivated by these benefits, we propose a novel PASS-aided AirComp system that introduces new design degrees of freedom through flexible pinching antenna (PA) placement. To improve performance, we consider a mean squared error (MSE) minimization problem by jointly optimizing the PA position, transmit power, and decoding vector. To solve this highly non-convex problem, we propose an alternating optimization based framework with Gauss-Seidel based PA position updates. Simulation results show that our proposed joint PA position and communication design significantly outperforms various benchmark schemes in AirComp accuracy.

Figures

Figures reproduced from arXiv: 2505.07559 by the authors.

**Figure 1.** Schematic of PASS-aided AirComp. We consider a PASS-aided AirComp system operating over an MAC. Specifically, a BS is equipped with M parallel dielectric waveguides, each equipped with N PAs, and aims to aggregate information from a set of K ≥ 1 users, denoted by K , {1, . . . , K}, where each device is equipped with a single antenna. Consider a three-dimensional (3D) coordination system, where the users are unifor… view at source ↗

**Figure 2.** (a) Convergence performance of our proposed desig [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Analytical Optimization for Antenna Placement in Pinching-Antenna Systems
cs.IT 2025-07 conditional novelty 4.0 of 10

For fairness-based OMA, the optimal pinching-antenna location is the mean of users' x-coordinates and does not depend on their distance from the waveguide; for NOMA it moves exponentially toward the user nearest the w...
A Gradient Meta-Learning Joint Optimization for Beamforming and Antenna Position in Pinching-Antenna Systems
cs.IR 2025-06 conditional novelty 4.0 of 10

A gradient meta-learning algorithm with two unrolled neural networks jointly optimizes beamforming and pinching-antenna positions, reporting 5.6 bits/s/Hz weighted sum rate and a 32.7% gain over alternating optimizati...
MIMO Pinching-Antenna-Aided SWIPT
cs.IT 2025-06 conditional novelty 4.0 of 10

A joint beamforming and pinching-antenna position optimization for MIMO SWIPT is proposed, using WMMSE inner iterations and grid-search position updates.

Reference graph

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Reviewed August 15, 2026 · model on record in the stance chip above.

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